docs: def helical_turbulent_fd_Schmidt(Re, Di, Dc, roughness=0):
      r'''Calculates Darcy friction factor for a fluid flowing inside a curved 
      pipe such as a helical coil under turbulent conditions, using the method of 
      Schmidt [1]_, also shown in [2]_.
      
      For :math:`Re_{crit} < Re < 2.2\times 10^{4}`:
      
      .. math::
          f_{curv} = f_{\text{str,turb}} \left[1 + \frac{2.88\times10^{4}}{Re}
          \left(\frac{D_i}{D_c}\right)^{0.62}\right]
          
      For :math:`2.2\times 10^{4} < Re < 1.5\times10^{5}`:
          
      .. math::
          f_{curv} = f_{\text{str,turb}} \left[1 + 0.0823\left(1 + \frac{D_i}
          {D_c}\right)\left(\frac{D_i}{D_c}\right)^{0.53} Re^{0.25}\right]
  
      Parameters
      ----------
      Re : float
          Reynolds number with `D=Di`, [-]
      Di : float
          Inner diameter of the coil, [m]
      Dc : float
          Diameter of the helix/coil measured from the center of the tube on one
          side to the center of the tube on the other side, [m]
      roughness : float, optional
          Roughness of pipe wall [m]        
  
      Returns
      -------
      fd : float
          Darcy friction factor for a curved pipe [-]
  
      Notes
      -----    
      Valid from the transition to turbulent flow up to 
      :math:`Re=1.5\times 10^{5}`. At very low curvatures, converges on the
      straight pipe result.
  
      Examples
      --------
      >>> helical_turbulent_fd_Schmidt(1E4, 0.01, .02)
      0.08875550767040916
  
      References
      ----------
      .. [1] Schmidt, Eckehard F. "Wärmeübergang Und Druckverlust in 
         Rohrschlangen." Chemie Ingenieur Technik 39, no. 13 (July 10, 1967): 
         781-89. doi:10.1002/cite.330391302.
      .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and 
         Correlations for Convection Heat Transfer and Pressure Losses in 
         Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
         (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
      '''
      fd = friction_factor(Re=Re, eD=roughness/Di)
      if Re < 2.2E4:
          return fd*(1. + 2.88E4/Re*(Di/Dc)**0.62)
      else:
          return fd*(1. + 0.0823*(1. + Di/Dc)*(Di/Dc)**0.53*Re**0.25)